Towards a Highly Sensitive Piezoelectric Nano-Mass Detection—A Model-Based Concept Study

sensors Communication Towards a Highly Sensitive Piezoelectric Nano-Mass Detection—A Model-Based Concept Study Jens Twiefel 1,* , Anatoly Glukhovkoy 2, Sascha de Wall 2, Marc Christopher Wurz 2, Merle Sehlmeyer 3, Moritz Hitzemann 3 and Stefan Zimmermann 3 1 Institute of Dynamics and Vibration Research, Leibniz Universität Hannover, An der Universität 1 Geb. 8142, 30823 Grabsen, Germany 2 Institute of Micro Production Technology, Leibniz Universität Hannover, An der Universität 2, 30823 Grabsen, Germany; [email protected] (A.G.); [email protected] (S.d.W.); [email protected] (M.C.W.) 3 Institute of Electrical Engineering and Measurement Technology, Leibniz Universität Hannover, Appelstr. 9A, 30167 Hannover, Germany; [email protected] (M.S.); [email protected] (M.H.); [email protected] (S.Z.) * Correspondence: [email protected]; Tel.: +49-511-762-4167 Abstract: The detection of exceedingly small masses still presents a large challenge, and even though very high sensitivities have been archived, the fabrication of those setups is still difficult. In this paper, a novel approach for a co-resonant mass detector is theoretically presented, where simple fabrication is addressed in this early concept phase. To simplify the setup, longitudinal and bending vibrations were combined for the first time. The direct integration of an aluminum nitride (AlN) piezoelectric element for simultaneous excitation and sensing further simplified the setup. The feasibility of this concept is shown by a model-based approach, and the underlying parameter Citation: Twiefel, J.; Glukhovkoy, A.; de Wall, S.; Wurz, M.C.; Sehlmeyer, dependencies are presented with an equivalent model. To include the geometrical and material M.; Hitzemann, M.; Zimmermann, S. aspects, a finite element model that supports the concept as a very promising approach for future Towards a Highly Sensitive nano-mass detectors is established. Piezoelectric Nano-Mass Detection— A Model-Based Concept Study. Sensors Keywords: piezoelectric sensors; nano-mass detection; inertial balance; resonance systems; nano/micro- 2021, 21, 2533. https://doi.org/ electro-mechanical-system; N/MEMS; co-resonance 10.3390/s21072533 Academic Editor: Christopher Oshman 1. Introduction The detection of weight is an important measurement task that has been performed Received: 2 March 2021 for thousands of years. Over time, precision and repeatability has dramatically improved. Accepted: 2 April 2021 Published: 4 April 2021 However, the measurement of exceedingly small masses—of the order of the atomic mass unit Dalton—is still a great challenge, even today. An important method for the detection Publisher’s Note: MDPI stays neutral of the smallest masses is the use of resonance modes, wherein the resonance frequency is with regard to jurisdictional claims in detuned by the mass to be detected. This method was first described in [1] in 1959 and has −10 published maps and institutional affil- been since then cited more than 9000 times. At that time, an accuracy of 10 g was already iations. archived with eigenfrequencies in the order of 10 MHz. Such an inertial balance utilizes the piezoelectric effect of the vibrating element, which is exited at a fundamental resonance via a closed loop control (e.g., [2]). This can be realized by either a phase-locked-loop or a self-oscillating circuitry. The frequency dependence of the resonance on the analyte mass is due to the ratio of analyte mass to the effective mass of the resonator; the highest sensitivity Copyright: © 2021 by the authors. Licensee MDPI, Basel, Switzerland. is obtained when both masses are similar in weight. Consequently, research in this field This article is an open access article has focused on even smaller and lighter resonator structures while aiming for better mass distributed under the terms and resolutions. The smallest known resonators are carbon nanotubes, with flexural mode conditions of the Creative Commons resonances in the GHz range that allow for yoctogram mass resolutions [3]. However, the Attribution (CC BY) license (https:// constantly decreasing sizes bring two major challenges: first, the fabrication gets more creativecommons.org/licenses/by/ complicated and therefore more expensive, making reproducibility difficult; second, the 4.0/). vibration measurement increases in complexity with decreasing structure size. Sensors 2021, 21, 2533. https://doi.org/10.3390/s21072533 https://www.mdpi.com/journal/sensors Sensors 2021, 21, 2533 2 of 15 In recent years, many research groups have worked on improving inertial balances, as listed in Table1. Various concepts of actuation and mass sensing have been evaluated including inductive, electrostatic, piezoelectric, and piezoresistive methods [4]. The max- imum obtained resolution was 10−24 g [5,6] at temperature levels from 5 to 300 K and ambient pressures of 10−10 to 10−5 Torr. Selected excitation and measurement methods are described below as examples. In the inductive method, a nano-resonator is placed in a magnetic field and a broadband alternating current is passed through the resonator so that the Lorentz force excites oscillation. The oscillation, in turn, induces a voltage that is amplified and measured to record the oscillation. A disadvantage, however, is the superposition of the measurement signal and the excitation. With the aid of special circuit variants, the feedback effect of the exciting signal on the measurement signal can be reduced [7,8]. Table 1. Selected publications on resonant nano-mass detection systems. Beam Measurement Material Resolution [g] ! [MHz] Co-Resonant Excitation Support 0 Principle [9] Silicon single-sided 5.5 × 10−15 1...10 - photothermal interferometer [10] Silicon double-sided n.a. 1000 - capacitive capacitive [11] SiC double-sided 2.53 × 10−18 32.8 - capacitive capacitive [12] CNT single-sided 1.3 × 10−22 328.5 - capacitive capacitive [13] CNT double-sided 2.5 × 10−20 125 - capacitive reflection [14] SiC double-sided n.a. 428 - capacitive capacitive [5] CNT double-sided 1.7 × 10−24 2000 - capacitive reflection [6] CNT single-sided 1.7 × 10−24 12 × 104 - capacitive reflection [15] Graphene double-sided 1.41 × 10−21 1.1 + piezoelectric piezoresistive [16] Silicon double-sided 1.7 × 10−21 20...120 + capacitive piezoresistive [17] Nano-crystalline single-sided 10−18 12 × 103 + capacitive reflection [18] Silicon single-sided 10−12 1.1 + piezoelectric piezoelectric In the electrostatic method, a nano-resonator is excited by an electrostatic field. A voltage between the nanostructure and electrodes, which are arranged in parallel, usually generates the field. In the case, either a broadband source or a source with an adjustable frequency can serve as the voltage source, whereby the frequency must be monitored for the latter, e.g., via a phase-locked loop. The resonant frequency is detected by measuring the change in capacitance between the nano-resonator and the counter electrode. The capacitance change can be measured by measuring the frequency of the displacement current at the capacitor with a transimpedance amplifier [4,7,19]. Self-oscillating active electrical circuits that integrate the nano-resonator circuitry are also used. Another method for determining the resonant frequency is based on the reflection measurement at an integrated transistor, which consists of a semiconducting nano-resonator that is mechanically clamped and electrically contacted on both sides with a counter electrode as gate. The reflection of an alternating signal at the electrical RLC resonant circuit with the integrated nano-transducer is then measured. Particle adsorption at the nano-resonator leads to a change in resistance and capacitance at a constant voltage between the gate and the oscillator and thus to a change in the reflection. However, this method requires a complex design of the nano-resonator as a transistor [20,21]. Other methods for measuring oscillations are based on optical interferometers in which an incident light beam is reflected by the nano-oscillator and superimposed with a reference beam. Based on the time-varying interference pattern, the vibration can be analyzed. The excitation of the nano-resonator can also be done photothermally with a laser by heating and expanding the nanostructure [9,22]. Piezoelectric methods, e.g., see [18], are based on the mechanical excitation of the nano-resonator via the deformation of piezoelectric nanostructures when a voltage is applied. Similar to electrostatic methods, the electrical voltage for vibration excitation can Sensors 2021, 21, x FOR PEER REVIEW 3 of 15 reference beam. Based on the time-varying interference pattern, the vibration can be analyzed. The excitation of the nano-resonator can also be done photothermally with a laser by heating and expanding the nanostructure [9,22]. Sensors 2021, 21, 2533 Piezoelectric methods, e.g., see [18], are based on the mechanical excitation 3of of the 15 nano-resonator via the deformation of piezoelectric nanostructures when a voltage is applied. Similar to electrostatic methods, the electrical voltage for vibration excitation can be begenerated generated via via a self-oscillating a self-oscillating active active electrical electrical circuit, circuit, e.g., e.g., see see [23]. [23 The]. The piezoelectric piezoelectric ap- approachproach of ofvibration vibration excitation excitation and and measuring measuring the the resonant resonant frequency frequency was was applied applied in this in thisstudy.

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